Key traitor is naughty youngster (4)

I believe the answer is:

brat

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'naughty youngster' is the definition.
'brat' can be an answer for 'youngster' (brat is a kind of youngster). I am unsure of the 'naughty' bit.

'key traitor' is the wordplay.
'key' becomes 'b' (eg B major, musical key).
'traitor' becomes 'rat' (rat can mean a treacherous person).
'b'+'rat'='BRAT'

'is' acts as a link.

Can you help me to learn more?

(Other definitions for brat that I've seen before include "Unpleasant child" , "Mervyn -- (Titus Groan)" , "Spoilt kid" , "Marie ---, birth-control pioneer" , "Little terror" .)

I've seen this clue in The Mirror.

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